NStar, a gold mining firm, has a current market capitalization of $ $300$ million with $80$ million shares outstanding. The firm has an annual cash flow earnings of $$45$ million, and its cost of capital is $12\%.$ NStar is considering taking over Sarecan Corp which has $20$ million shares outstanding with a market capitalization of $ $35$ million and annual cash flow earnings of $$2\mathrm{.}5$ million. The cost of capital for Sarecan is $10\%.$ The takeover is expected to result in an annual additional cash flow of $ $0\mathrm{.}95$ million in the first year, which is expected to remain constant in perpetuity. The cost of capital for synergies is $12\%.$ NStar is considering two different options to finance the take over $($i$)$ a cash offer with a $28\%$ premium relative to its market price $($ii$)$ a share swap of $1$ share of NStar for every $2$ shares of Sarecan.

a$.$ Calculate $($i$)$ overall gain $($ii$)$ gain to NStar shareholders and $($iii$)$ gain to Sarecan shareholders if the cash offer is made

b$.$ Calculate $($i$)$ gain to NStar shareholders and $($ii$)$ gain to Sarecan shareholders if the share$-$swap offer is made

c$.$ At what cash offer price $($cash offer$)$ would this be a zero NPV investment for NStar?